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Date: Fri, 05 Sep 2014 16:10:24 0400 From: Bill Cox <waywardgeek@...hershed.org> To: discussions@...swordhashing.net Subject: Re: [PHC] A review per day  skipping Makwa BEGIN PGP SIGNED MESSAGE Hash: SHA1 So, I was unable to resist reviewing Makwa in depth. It's super cool! I have a few comment to finish my review, unless there is followon discussion. First, Makwa has potential that even the author probably may not suspect. This is because his estimate than an ASIC attack would be ineffective is wrong, by a very large margin. An ASIC attack will be devastatingly faster against Makwa than any memoryhard entry in the competition. I'll discuss the outline of an ASIC attack at the end. However, Makwa hashes can be remotely computed on untrusted ASIC based Makwa servers securely, unlike any other password hashing system. Once ASIC based servers come online in the cloud, everyone will be able to benefit from them. Makwa is in the unique position that a solid ASIC attack is probably a *good* thing. Some notes I made:   Step 4 on page 8 scrambles V, so that step 5 has a V which may contain 0x1 values, so the 0x1 is not easily seen as a terminator. Should step 4 be removed?   Step 8 generates Hs(m) which is trivially determined to be nonrandom. Should he simply append a counter and hash for each output word instead?   Note: 10 byte output hash is recommended as the minimum, but if that is used, we will be able to find input collisions with only 2^40 tries. This could be used by an attacker to exploit bugs in some cases, so I would prefer to use 20 byte output as the minimum   My preference would be to use a Catenalike garlic wrapper to do offline work increase without storing all 2048 bits of the hash. This is not as efficient but 2048 bits is a lot to store, and I am not convinced that 4096 bits is a bad idea.   If we do pre and post hashing, supporting to 4096 isn't too ugly   Page 18, step 2, is that really x^2? It makes sense to me if it's just x.   Experimentally, I see that the only primes that have full cycle length are "safe" primes congruent to 3 mod 4 For Makwa to be secure, we need some assurance that picking a random x value and squaring it many times continues to do useful work, and will not cycle back on itself quickly. If it does cycle back too soon, and an attacker can determine the cycle length, he likely can determine the secret values p and q, breaking the system. Choosing random safe primes that are congruent to 3 mod 4 sometimes leads to cycle lengths less than p or q, potentially weakening security. Therefore, I recommend using what I'm calling "solid" Makwa primes. The must be safe primes congruent to 3 mod 4 which also have (p3)/4 prime. Experimentally, the group structures are very uniform when this is true, and the minimum cycle length any randomly chosen x will have is (p3)(q3)/16. There are always 4 different sizes of groups: 1, groups of size either (p3)/4 or (p3)/2, groups of size (q3)/4 or (q3)/2, and groups of size (p3)(q3)/16 or (p3)(q3)/8. The total number of residues is always 3 + (p3) + (q3) + (p3)(q3)/4. The chance of picking a random residue (by squaring a random x), and getting anything but the largest subgroup is about: 4*(p + q)/(p*q) Assuming p and q are about the same size, this is just: 8/sqrt(n) For n being on the order of 2^2048, this is 8/(2^1024), meaning this will *never* happen anytime in the life of our universe, unless someone monkey's with the random number generator (or if there are bugs). The security of Makwa when using solid Makwa primes seems to be limited by the factoring problem, of determining p*q given n. The Knapsack problem used for obfuscating X when delegating is a random instance of an NPComplete problem I've played with quite a bit, and Makwa's version looks solid to me. ASIC Attack   Both attackers and Makwa cloud based authentication servers will g high password hashing throughput compared to a user's computer. The 2048bit multiplies, SFAIK, are not even the hardest part. The mod n takes up more area. I estimate a 1bit carry save adder with an extra XOR (for Booth encoding) in 22nm to be about 1u^2. While that is a WAG, I arrive at it by taking a carry save adder in a structured ASIC I designed in .35u, and putting about 16 of them in a block about 40ux40u. That comes out to exactly 100u^2 each. Shrinking to 35nm gives me a 1u^2 cell, and since I have to go to finfets and all sorts of crud down at this size, I assume I lose about 1 process generation vs a straight shrink. Therefore, 1u^2 at 22nm, the same process as my Ivy Bridge CPU :) I can build the Booth encoded circuit with an array of 2048 by 1024 of these cells, which is 2mm by 1mm. I'm not sure if I would want to put more than 1 per ASIC, as when I introduce a 1024deep pipeline, diagonally through the multiplier and modulus circuit, this thing will produce a 2048bit multiplication/mod result every clock. This needs to be built in a lowpower process, because running a Makwa ASIC box will probably be dominated by power cost. Also, the ASIC will generate insane amounts of power compared to most chips, because of the massive fully pipelined data paths. These chips will run as hot as your GPU at full steam. 2mm^2 for the multiplier is no biggie. I could afford several of them. However, the mod n operation also has to be pipelined, and the simple implementation I understand has 2048 subtractors and comparitors. This is 2X to 3X larger than the multiplier, so let's call it a total of 8mm^2 per hashing engine. Comparing to my highend Intel CPU, each engine should easily run at 3.4GHz. The trick with this ASIC is optimizing the ability to suck power out. There are some packages, like QFN, which do a decent job sucking power out through the back of the die. The cost under $1. I would be tempted to consider placing just one instance of this ASIC hashing core in a tiny ASIC to see if this leads to the lowest total cost of ownership. The other highpower option is flipchip, at about $100/package, if things haven't changed much. In that case, I could suck 70W out of one ASIC with a bunch of Makwa cores on it. I'd guess at least 10 cores could be cooled enough, but that's a shot in the dark. I believe it will be power limited, not area limited. To be cost effective, each ASIC should be computing 1024 password hashes in parallel at peak load. Each computation would be many times faster than a CPU based approach because the multiplier and modulus are fully implemented with 2048bit data paths. I'm not sure what the CPU can do a 2048bit multiply/mod operation in. The ASIC should be able to do it in about 1/3 us, and it does that on about 1000 passwords in parallel at the same time. With work factors up to 1,000,000, that would take up to 1/3 second latency, with a throughput of about 3000 password hashes per second per core. How fast would my CPU do this? Can we use my 4 CPUs with their 4 128 or 256(Haswell) bit data paths to accelerate it? I'll bet Samuel Neves or Alexander could just tell us the answer :) For this to be an effective strategy, Makwa delegation is a *must*. Users trying to do a 1 second 1,000,000 work factor on their own CPUs will wind up killing the job before it finishes. For effective protection, delegation to an ASIC based Makwa farm is the only thing that makes sense to me. That's all I have for now for Makwa! I hope my mathematical analysis didn't totally suck! It's definitely out of my comfort zone... Bill BEGIN PGP SIGNATURE Version: GnuPG v1 iQIcBAEBAgAGBQJUChisAAoJEAcQZQdOpZUZ6koQAKbjKaFJ1dssaUqxoXW06DVb 865WxPcp7FVR+5scwXuEqRUrBDkoPLvOSmihx9+jI8oI1vo6F5xHlEVumQGjUCfK z7PctgkpwUBmE5e2sclxShqIhUKG83R8cBo+ZBaXptOPnK8JBk/Z+Eudl6OBTVP3 XcIYnn65g9CNz7kxMXO2hoR8nw47YTaR57jiB8iLSRWHKxW9GJ1vG4YcwGZAEYvX df/sTzYnNHz/h7aYG7Ic7qQjzYZ9T7RRSQs4DqgNSZO+UZNS1qX/evfidG6q4OzH Vedn9sf1HHhUYmm+agN46tXHbpdrVqtkF2T2KPWGnt4+QEK8IKj4tqn9s0tlLOwe H0ruGz65RSPueisyeYc+5/4X515hTB049tYnJ9s/cU4sZEN5JP+fAJrXj6J+C/VP epK1QC02AWQo3Au/tBHCyakGUwYHjlPc/h6GcO6fk8CIe/cOElZEbtOEifSlAv65 /xXyrMmRzPvJ+viT7ff0jZSlQkqCOkiMzhJtWCLDgQcKF50FqfVr+u5x3t3bSNdl tg5aAt13QSdG951IZu9EiXrav3joLEk6jjUJNvRl0fQS4e6T0FXU/uDv6nm0BnlQ 83sF6alf39ODgp0PPSKxgdKX2RuZ/EOZteaZWPLri+6t1paBjsTTbAGQpdL1qJJB mT6Vp4OtjyV7ISlvzZvr =Yllu END PGP SIGNATURE
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